Rational mixed Tate motivic graphs

Owen A Patashnick, Susama Agarwala

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Abstract

In this paper, we study the combinatorics of a subcomplex of the Bloch-Kriz cycle complex [4] used to construct the category of mixed Tate motives. The algebraic cycles we consider properly contain the subalgebra of cycles that correspond to multiple logarithms (as defined in [12]). We associate an algebra of graphs to our subalgebra of algebraic cycles. We give a purely graphical criterion for admissibilty. We show that sums of bivalent graphs correspond to coboundary elements of the algebraic cycle complex. Finally, we compute the Hodge realization for an infinite family of algebraic cycles represented by sums of graphs that are not describable in the combinatorial language of [12].
Original languageEnglish
Pages (from-to)451-515
Number of pages55
JournalAnnals of K-Theory
Volume2
Issue number4
Early online date16 Nov 2017
DOIs
Publication statusPublished - 1 Dec 2017

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